Simplify to lowest terms. $\dfrac{40}{90}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 90? $40 = 2\cdot2\cdot2\cdot5$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(40, 90) = 2\cdot5 = 10$ $\dfrac{40}{90} = \dfrac{4 \cdot 10}{ 9\cdot 10}$ $\hphantom{\dfrac{40}{90}} = \dfrac{4}{9} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{40}{90}} = \dfrac{4}{9} \cdot 1$ $\hphantom{\dfrac{40}{90}} = \dfrac{4}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{90}= \dfrac{2\cdot20}{2\cdot45}= \dfrac{2\cdot 5\cdot4}{2\cdot 5\cdot9}= \dfrac{4}{9}$